Answer:
x = 1 ±2sqrt(5)
Step-by-step explanation:
2x^2-4x-9=29
Add 9 to each each side
2x^2-4x-9+9=29+9
2x^2-4x=38
Divide by 2
2/2x^2-4/2x=38/8
x^2 -2x =19
Complete the square
x^2 -2x + (-2/2)^2 = 19 +(-2/2)^2
x^2 -2x +1 = 19+1
(x-1)^1=2 = 20
Take the square root of each side
sqrt((x-1)^2) = ±sqrt(20)
x-1 = ±sqrt(20)
Add 1 to each side
x-1+1 = 1 ±sqrt(20)
x = 1 ±sqrt(20)
Simplifying the square root of 20
x = 1 ±sqrt(4)sqrt(5)
x = 1 ±2sqrt(5)
Formula for amount for compound interest:
Amount, A = P(1 + r/100)^n
Where r is rate, P is principal, and n is the number of years.
P = 2000, r = 5, n = t years.
A = 2000( 1 + 5/100)^t
A = 200(1+0.05)^t
A = 2000(1.05)^t
A(t) = 2000(1.05)^t
Answer:
Here for the comments .
Step-by-step explanation:
Ya, calculus and related rates, such fun!
everything is changing with respect to t
altitude rate will be dh/dt and that is 1cm/min
dh/dt=1cm/min
area will be da/dt which is increasing at 2cm²/min
da/dt=2cm²/min
base=db/dt
alright
area=1/2bh
take dervitivie of both sides
da/dt=1/2((db/dt)(h)+(dh/dt)(b))
solve for db/dt
distribute
da/dt=1/2(db/dt)(h)+1/2(dh/dt)(b)
move
da/dt-1/2(dh/dt)(b)=1/2(db/dt)(h)
times 2 both sides
2da/dt-(dh/dt)(b)=(db/dt)(h)
divide by h
(2da/dt-(dh/dt)(b))/h=db/dt
ok
we know
height=10
area=100
so
a=1/2bh
100=1/2b10
100=5b
20=b
so
h=10
b=20
da/dt=2cm²/min
dh/dt=1cm/min
therefor
(2(2cm²/min)-(1cm/min)(20cm))/10cm=db/dt
(4cm²/min-20cm²/min)/10cm=db/dt
(-16cm²/min)/10cm=db/dt
-1.6cm/min=db/dt
the base is decreasing at 1.6cm/min
Answer:
14
Step-by-step explanation:
The diameter is the length from one point on the circle to another, passing through the center. The <em>radius </em>is the length from a point on the circle to its center, so we can always find the diameter by doubling the radius. In this case, with a radius of 7, our diameter is 7 · 2 = 14
